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Linearization of bounded holomorphic mappings on Banach spaces. (English) Zbl 0747.46038
The author shows that for every open subset $U$ of a Banach space there exists a unique Banach space $G\sp \infty(U)$ and a holomorphic mapping $g\sb u:U\to G\sp \infty(U)$ such that every Banach valued bounded holomorphic function on $U$ can be written as a composition of $g\sb u$ and a Banach valued continuous linear mapping on $G\sp \infty(U)$. This gives a linearization of bounded holomorphic mappings and shows that $H\sp \infty(U)$ has the structure of a dual Banach space. Applications to the study of holomorphic mappings of compact type, the approximation property and polynomials are given using this linearization result.
Reviewer: S.Dineen

46G20Infinite dimensional holomorphy
46E50Spaces of differentiable or holomorphic functions on infinite-dimensional spaces
46B28Spaces of operators; tensor products; approximation properties
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